A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies

Abstract

In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce \(\mathcal {ALCH}^{\bullet }\), a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics for \(\mathcal {ALCH}^{\bullet }\) in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking \(\mathcal {ALCH}^{\bullet }\) knowledge-base consistency that always terminates and we show that it is sound and complete w.r.t. our preferential semantics. The general framework we here propose can serve as the foundation for further exploration of non-monotonic reasoning in description logics and similarly structured logics.

Keywords

Description logic defeasible reasoning typicality tableaux

This work was the recipient of the first Louis Couturat Logic Prize (France, 2018). It was then presented at the Universal Logic Contest at UNILOG 2018 in Vichy and subsequently won the first Universal Logic Prize.

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Acknowledgements

I am grateful to Richard Booth, Arina Britz, Giovanni Casini, Fred Freitas and Tommie Meyer for many stimulating discussions on the topics of the present paper. I would like to thank Jean-Yves Béziau for encouraging me to participate in the logic contests. I am also grateful to the Universal Logic Prize jury members Hartry Field, Michèle Friend, Grzegorz Malinowski, Ahti-Veikko Pietarinen, Peter Schroeder-Heister, Göran Sundholm and Leon van der Torre for their appreciation of this work, and to the Louis Couturat Logic Prize anonymous referees for their constructive comments on an earlier version of the present paper. This work was partially supported by the project Reconciling Description Logics and Non-Monotonic Reasoning in the Legal Domain (PRC CNRS–FACEPE France–Brazil). Special thanks to Sihem, without whose support this work would have not come to existence, and to whom I dedicate the logic prizes it has won.